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Published online by Cambridge University Press: 05 June 2012
Voronoi diagrams are very useful structures, frequently encountered in several disciplines because they model growth processes and distance relationships between objects: it is not surprising to see them appear in the study of crystal growth or in studies on the great structures of the universe. In nature, they can be observed in crystalline structures, on the shell of a turtle, or on the neck of a reticulate giraffe.
Voronoi diagrams are very closely related to the geometric structures encountered so far: polytopes, triangulations, and arrangements. Their mathematical properties are particularly numerous and interesting. Chapter 17 is entirely devoted to Voronoi structures with a Euclidean metric, whereas other metrics are studied in chapter 18. Chapter 19 presents results specific to dimension 2 that have no analogue in higher dimensions.
Voronoi diagrams can also be used as data structures to solve numerous problems: nearest neighbors and motion planning are two outstanding instances. Several examples are given in the exercises and throughout chapter 19.
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